Quantitative research of generalized tautologies in n-valued propositional logic L_n~*

By means of the infinite product of evenly distributed probability spaces,the proportion of the class of valuation which satisfies v(A)≥ζ(or v(A)ζ,where ζ∈) in the set of all valuations is considered and the concepts of ζ-truth degree and ζ+-truth degree in n-valued R0-propositional logic system Ln  are introduced in order to double-grade the concept of tautology.Also,the theories of σ-(ζ-tautology) and σ-(ζ+-tautology) are defined.Moreover,relationships between ζ-truth degree(ζ+-truth degree) and generalized tautology together with the graded generalized tautology are discussed and the general reference rules endowed with ζ-truth degree are proved.